I always get bored at the barren desert part with the unfitting music.
Uh... what?
There's only one "desert" in Chrono Trigger that I can think of, and it's in a sidequest at the very end of the game.
seeing as how he used the word barren, he's probably talking about the wasteland future
which is the first place you go to, i think, at the start of the game.
Third/fourth, depending on how you count it. You start in 1000 AD, go back to 600 AD for the Marle/Leene quest, back to 1000 AD for the trial, then to 2300 AD.
And I dunno, that place doesn't scream "desert" to me.